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<p>The rapid development of neural quantum states (NQS) has established it as a promising framework for studying quantum many-body systems. In this work, by leveraging the transformer-based architectures and developing efficient optimization algorithms, we achieve the state-of-the-art results for the doped two-dimensional (2D) Hubbard model, arguably the minimum model for high-Tc superconductivity. Interestingly, we find different attention heads in the NQS ansatz can directly encode correlations at different scales, making it capable of capturing long-range correlations in strongly correlated systems. With these advances, we find evidence for the half-filled stripe in the ground state of 2D Hubbard model with the next nearest neighboring hopping, consistent with experimental observations in cuprates. Our work establishes NQS as a powerful tool for solving challenging many-fermions systems.</p>

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Solving the Hubbard model with neural quantum states

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年6月22日

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  • Yuntian Gu,
  • Wenrui Li,
  • Heng Lin,
  • Bo Zhan,
  • Ruichen Li,
  • Yifei Huang,
  • Di He,
  • Yantao Wu,
  • Tao Xiang,
  • Mingpu Qin,
  • Liwei Wang,
  • Dingshun Lv

摘要

The rapid development of neural quantum states (NQS) has established it as a promising framework for studying quantum many-body systems. In this work, by leveraging the transformer-based architectures and developing efficient optimization algorithms, we achieve the state-of-the-art results for the doped two-dimensional (2D) Hubbard model, arguably the minimum model for high-Tc superconductivity. Interestingly, we find different attention heads in the NQS ansatz can directly encode correlations at different scales, making it capable of capturing long-range correlations in strongly correlated systems. With these advances, we find evidence for the half-filled stripe in the ground state of 2D Hubbard model with the next nearest neighboring hopping, consistent with experimental observations in cuprates. Our work establishes NQS as a powerful tool for solving challenging many-fermions systems.